> At near lightspeed, a pea-sized rock will kill your spaceship
Why travel in a spaceship? If there's 100,000 starless planets for every star in the galaxy, then travel between stars on one of them instead. Build the habitations 10 km below water to avoid radiation. Travel at 0.1% light speed instead and get to the nearest star in 5000 yrs. Enjoy the journey, and slip into an orbit around the target star.
Speaking of pea-sized rocks, periodically fire one laden with electronics/optics/quantumics at the target star at near light speed and receive its transmissions for recon.